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Chapter 6: Q38E (page 307)

For two invertible nxnmatrices A and B , what is the relationship between adj(A),adj(B),andadj(AB)?

Short Answer

Expert verified

Therefore, the relationship of adjA,adjBandadjABis given by,

adjAB=adjBadjA.

Step by step solution

01

Matrix Definition. 

Matrix is aset of numbers arranged in rows and columns so as to form a rectangulararray.

The numbers are called the elements, or entries, of the matrix.

If there are m rows and n columns, the matrix is said to be an 鈥渕 by n鈥� matrix, written 鈥�.mxn鈥�

02

To find the relationship of  and

To find the relationship,

It applies,

adjAB=det(AB(AB)-1 adjAB=detAdetBB-1A-1adjAB=detBB-1detAA-1ThereforeadjAB=adjBadjA.

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Most popular questions from this chapter

Show that an nxn matrixAhas at least one nonzero minor if (and only if) rank(A)鈮�n-1.

Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.

3.[13241648130026412]

det(4A)=4detAfor all4脳4 matricesA.

There exists a nonzero4脳4 matrixAsuch thatdetA=detA(4A).

For every nonzero2脳2 matrix A there exists a 2脳2 matrix B such that det(A+B)鈮�detA+detB.
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